Nonlinear Regression Act1
Exponential Curve Fitting
Directions: In this activity we will be exploring Exponential functions with Statcrunch or Minitab.
For StatCrunch, go to the Stat menu, click on “regression”, then “simple linear”. Put in the x and y
variables. Under the “transformation” section click on “Natural Logarithm: log(y)”. Make sure to click
on fitted line plot for the scatterplot. Keep in mind that even though the formula says “log” it is
actually natural log (LN).
For Minitab, you will need to go to the “Statistics” menu in Minitab. Then click on “regression” and
then fitted line plot. Make sure to click on “log y” under the options button. Keep in mind that
Minitab numbers will be different from Statcrunch. Minitab is using Log base 10.
1. Open the Module 4 Data Sets in Excel. Copy and paste the years since 1995 and wind power
into Statcrunch or Minitab. This data gives the number of years since 1995 and the world wide
wind power capacity in MW (megawatts).
a) Use Minitab or Statcrunch to make a scatter plot of the ordered pairs. Let the number
of years be the explanatory variable and the wind power be the response variable. Does
the scatterplot look like an exponential model might fit? If so, would it be exponential
growth or exponential decay.
b) Now use the Log(y) transformation to find the exponential model that best fits the
curve. Do you think that the exponential curve fits the data well?
c) What was r 2 ? Write a sentence explaining the meaning of r 2 in this context.
d) Save your answers on your flash drive as well as the scatterplot with exponential curve,
the r 2 value, and the equation of the exponential curve (“Log y”) that the computer
found.
2. Open the Module 4 Data Sets in Excel. Copy and paste the month and retirement account
balance into Statcrunch or Minitab. The following data gives the balance in a retirement
account. The couple started with $78,000 in their account in 2010, and have been slowly
making withdrawals for their living expenses. The data gives the months since January 2010 and
the retirement account balance in thousands of dollars.
a) Use Minitab or Statcrunch to make a scatter plot of the ordered pairs. Let the months
be the explanatory variable and the retirement account balance be the response
variable. Does the scatterplot look like an exponential model might fit? If so, would it
be exponential growth or exponential decay.
b) Now use the Log(y) transformation to find the exponential model that best fits the
curve. Do you think that the exponential curve fits the data well?
c) What was r 2 ? Write a sentence explaining the meaning of r 2 in this context.
d) Save your answers on your flash drive as well as the scatterplot with exponential curve,
the r 2 value, and the equation of the exponential curve (“Log y”) that the computer
found.
3. Open the Module 4 Data Sets in Excel. Copy and paste the years since 1990 and the saving’s
account balance into Statcrunch or Minitab. The savings account was opened in 1990. The
following ordered pairs give the number of years since 1990 and the amount of money in a
savings account.
a) Use Minitab or Statcrunch to make a scatter plot of the ordered pairs. Let the number
of years be the explanatory variable and the savings account balance be the response
variable. Does the scatterplot look like an exponential model might fit? If so, would it
be exponential growth or exponential decay.
b) Now use the Log(y) transformation to find the exponential model that best fits the
curve. Do you think that the exponential curve fits the data well?
c) What was r 2 ? Write a sentence explaining the meaning of r 2 in this context.
d) Save your answers on your flash drive as well as the scatterplot with exponential curve,
the r 2 value, and the equation of the exponential curve (“Log y”) that the computer
found.
4. Open the Module 4 Data Sets in Excel. Copy and paste the metal distance and ultrasound
response into Statcrunch or Minitab. Ultrasound is used in a variety of applications. Let the
explanatory variable be the metal distance in millimeters and the response variable be the
ultrasound response.
a) Use Minitab or Statcrunch to make a scatter plot of the ordered pairs. Let the metal
distance the explanatory variable and the ultrasonic response be the response variable.
Does the scatterplot look like an exponential model might fit? If so, would it be
exponential growth or exponential decay.
b) Now use the Log(y) transformation to find the exponential model that best fits the
curve. Do you think that the exponential curve fits the data well?
c) What was r 2 ? Write a sentence explaining the meaning of r 2 in this context.
d) Save your answers on your flash drive as well as the scatterplot with exponential curve,
the r 2 value, and the equation of the exponential curve (“Log y”) that the computer
found.
5. The equations Statcrunch found had the Natural Log (base “e”) in them and the Minitab
equations had LOG (base 10) in them. Explain how this equation is actually describing an
exponential function and not a Logarithmic function?
6. A student wanted to map an exponential function model to the atomic defect and energy data
(See mod 4 data sets). Minitab and Statcrunch said “Error” and “Not Available”. The programs
were unable to find an exponential function to fit the data. Explain why this happened. What
does this tell us about data sets that cannot be modeled with exponential models?